So many overloads - pattern, complexity, atoms - can't we come up with new terms like schfinkledorfs? - but a very interesting question is - given an image of W x H pixels of 1 bit depth (on or off), one frame, how many "patterns" exist within this grid? When you think about it, it becomes an extremely difficult question to answer because within a static image you can have dupes, different sizes, dimensions, distortions, compressions, expansions, combo's... it's crazy. BUT, there is a pattern to the patterns - there's a mathematical description of them.
John > -----Original Message----- > From: Richard Loosemore [mailto:[EMAIL PROTECTED] > Sent: Thursday, May 08, 2008 11:18 AM > To: [email protected] > Subject: [agi] Re: pattern definition > > [EMAIL PROTECTED] wrote: > > Hello > > > > I am writing a literature review on AGI and I am mentioning the > > definition of pattern as explained by Ben in his work. > > > > "A pattern is a representation of an object on a simpler scale. For > > example, a pattern in a drawing of a mathematical curve could be a > > program that can compute the curve from a formula (Looks et al. 2004). > > My supervisor told me that "she doesn?t see how this can be simpler > than > > the actual drawing". > > > > Any other definition I could use in the same context to explain to a > > non-technical audience? > > > > thanks > > > > xav > > Xav, > > [I am copying this to the AGI mailing list because it is more > appropriate there than on Singularity] > > A more general definition of pattern would include the idea that there > is a collection of mechanisms that take in a source of information (e.g. > an image consisting of a grid of pixels) and respond in such a way that > each mechanism 'triggers' in some way when a particular arrangement of > signal values appears in the information source. > > Note that the triggering of each mechanism is the 'recognition' of a > pattern, and the mechanism in question is a 'recognizer' of a pattern. > (In this way of looking at things, there are many mechanisms, one for > each pattern). The 'particular arrangement of signal values' is the > pattern itself. > > Most importantly note that a mechanism does not have to trigger for some > exact, deterministic set of signal values. For example, a mechanism > could respond in a stochastic, noisy way to a whole bunch of different > arrangements of signal values. It is allowed to be slightly > inconsistent, and not always respond in the same way to the same input > (although it would be a particularly bad pattern recognizer if it did > not behave in a reasonably consistent way!). The amount of the > 'triggering' reaction does not have to be all-or-nothing, either: the > mechanism can give a graded response. > > What the above paragraph means is that the thing that we call a > 'pattern' is actually 'whatever makes a mechanism trigger', and we have > to be extremely tolerant of the fact that a wide range of different > signal arrangements will give rise to triggering ... so a pattern is > something much more amorphous and hard to define than simply *one* > arrangement of signals. > > Finally, there is one more twist to this definition, which is very > important. Everything said above was about arrangements of signals in > the primary information source ... but we also allow that some > mechanisms are designed to trigger on an arrangement of other > *mechanisms*, not just primary input signals. In other words, this > pattern finding system is hierarchical, and there can be abstract > patterns. > > This definition of pattern is the most general one that I know of. I > use it in my own work, but I do not know if it has been explicitly > published and named by anyone else. > > In this conception, patterns are defined by the mechanisms that trigger, > and further deponent sayeth not what they are, in any more fundamental > way. > > And one last thing: as far as I can seem this does not easily map onto > the concept of Kolmogorov complexity. At least, the mapping is very > awkward and uninformative, if it exists. If a mechanism triggers on a > possibly stochastic, nondeterminstic set of features, it can hardly be > realised by a feasible algorithm, so talking about a pattern as an > algorithm that can generate the source seems, to me at least, to be > unworkable. > > Hope that is useful. > > > > > Richard Loosemore > > > P.S. Nice to see some Welsh in the boilerplate stuff at the bottom of > your message. I used to work at Bangor in the early 90s, so it brought > back fond memories to see "Prifysgol Bangor"! Are you in the Psychology > department? > > ------------------------------------------- > agi > Archives: http://www.listbox.com/member/archive/303/=now > RSS Feed: http://www.listbox.com/member/archive/rss/303/ > Modify Your Subscription: > http://www.listbox.com/member/?&; > 2bb036 > Powered by Listbox: http://www.listbox.com ------------------------------------------- agi Archives: http://www.listbox.com/member/archive/303/=now RSS Feed: http://www.listbox.com/member/archive/rss/303/ Modify Your Subscription: http://www.listbox.com/member/?member_id=8660244&id_secret=101455710-f059c4 Powered by Listbox: http://www.listbox.com
